Simplify the following expression: $q = \dfrac{9}{5x + 4} \div \dfrac{10}{8x}$
Solution: Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{9}{5x + 4} \times \dfrac{8x}{10}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 9 \times 8x } { (5x + 4) \times 10}$ $q = \dfrac{72x}{50x + 40}$ Simplify: $q = \dfrac{36x}{25x + 20}$